454? M. E. Wilde on the U?itenableness of 



polarized perpendicular to the plane of incidence ; the former 

 (that is, of the ray in which the oscillations are at right angles 

 to the plane of incidence and to the direction of the ray) has 

 the following value : — 



sin (i-r) ^ 



sin (2-t-r) 5 K ' } 



and the latter (that is, of the ray in which the oscillations are 

 parallel to the plane of incidence and perpendicular to the 

 direction of the ray) the value* — 



tan (i-r) ^ , g . 



tan (i + r) ' 



At the upper limit of the layer of air, the angle of incidence i 

 is smaller than the angle of refraction r, the passage in this 

 case being from glass to air; the expression (1.) is therefore 

 positive. At the lower limit of the air-layer, on the contrary, 

 the angle i is greater than r, the passage in this case being 

 from air to glass ; and the same expression is consequently 

 negative. In the same way the expression (2.) changes its 

 sign according as it refers to the one or the other limit of 

 the air-layer; at the upper limit it is negative, and at the 

 lower limit it is positive. A change of sign, however, in the 

 velocity of oscillation is always accompanied by a reversion of 

 the direction of oscillation. Hence,, when a natural (unpo- 

 larized) ray, which as regards intensity may be considered as 

 composed of the two polarized rays mentioned above, is re- 

 flected at the lower boundary of the layer of air, a reversion 

 of the aether oscillations, as compared with their direction 

 after reflexion from the upper boundary, must take place, 

 which reversion, as regards the intensity of the reflected light, 

 has the same effect as if the difference of the paths traversed 

 by both rays was half an undulation (or in general an odd 

 number of semi-undulations) greater or less than it really is; 

 this however lender the sole condition that a layer of air exists 

 between the two glasses. If therefore a difference of half an 

 undulation has been heretofore assumed at the point where no 

 air exists between the glasses, the said assumption has been 

 made in direct opposition to the theory of undulation. 



If, on account of the reversion of the oscillation, I assume 

 the difference of the paths traversed by the interfering homo- 

 geneous rays half an undulation X (or an odd number of half 

 undulations) greater or less than it really is, then the sim- 

 plest expression for the intensity of the reflected light I find 



to be d cos r 



J = 4asin 2 27r — r , (3.) 



A, 



vol. xxii. p. 90. 



